Problem: $K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 7x + 1$ and $ KL = 2x + 11$ Find $JL$.
A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {7x + 1} = {2x + 11}$ Solve for $x$ $ 5x = 10$ $ x = 2$ Substitute $2$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 7({2}) + 1$ $ KL = 2({2}) + 11$ $ JK = 14 + 1$ $ KL = 4 + 11$ $ JK = 15$ $ KL = 15$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {15} + {15}$ $ JL = 30$